Shape Optimization for Acoustic Wave Propagation Problems

Abstract: Boundary shape optimization is a technique to search for an optimal shape by modifying the boundary of a device with a pre-speci?ed topology. We consider boundary shape optimization of acoustic horns in loudspeakers and brass wind instruments. A horn is an interfacial device, situated between a source, such as a waveguide or a transducer, and surrounding space. Horns are used to control both the transmission properties from the source and the spatial power distribution in the far-?eld (directivity patterns).Transmission and directivity properties of a horn are sensitive to the shape of the horn ?are. By changing the horn ?are we design transmission ef?cient horns. However, it is dif?cult to achieve both controllability of directivity patterns and high transmission ef?ciency by using only changes in the horn ?are. Therefore we use simultaneous shape and so-called topology optimization to design a horn/acoustic-lens combination to achieve high transmission ef?ciency and even directivity. We also design transmission ef?cient interfacial devices without imposing an upper constraint on the mouth diameter. The results demonstrate that there appears to be a natural limit on the optimal mouth diameter.We optimize brasswind instruments with respect to its intonation properties. The instrument is modeled using a hybrid method between a one-dimensional transmission line analogy for the slowly ?aring part of the instrument, and a ?nite element model for the rapidly ?aring part.An experimental study is carried out to verify the transmission properties of optimized horn. We produce a prototype of an optimized horn and then measure the input impedance of the horn. The measured values agree reasonably well with the predicted optimal values.The ?nite element method and the boundary element method are used as discretization methods in the thesis. Gradient-based optimization methods are used for optimization, in which the gradients are supplied by the adjoint methods.